Question

The number of square tiles required of size \[20cm\] to cover a square courtyard of area \[64{m^2}\] are
A.\[1598\]
B.1600
C.1605
D.1606

Answer 1

Hint: Here, we will use the formula for the area of a square, that is, \[{(side)^2}\]. Also, the area of the courtyard is given in \[{m^2}\] so we will have to convert the area into \[c{m^2}\] or we can convert the size of the tiles from cm to m.

Complete step-by-step answer:
We are given the size of the square tiles used and the area of the square courtyard to be covered.
The size of the square tile\[ = 20cm\]
The area of the square tile
\[
   = {(side)^2} \\
   = {(20)^2} \\
   = 400c{m^2} \\
\]
We will have to make the measures of the two areas same to find the number of the square tiles required, so we convert the area into \[c{m^2}\] from \[{m^2}\].
The Area of the square courtyard
\[
   = 64{m^2} \\
   = (64 \times 100 \times 100)c{m^2} \\
   = 6,40,000c{m^2} \\
\]
We are multiplying \[100\] twice in the area since
\[
  1m = 100cm \\
   \Rightarrow 1{m^2} = (100 \times 100)c{m^2} \\
\]
Therefore, the number of square tiles required to cover the square courtyard
\[
   = \dfrac{{6,40,000c{m^2}}}{{400c{m^2}}} \\
   = 1600 \\
\]\[\]

Thus, the answer is option B.

Note: There might be variations of this problem in which instead of two squares, it is possible that we are given one square and one rectangle. We will simply use the formula \[(length \times breadth)\]to find the area of the rectangle and then divide it by the area of the square or vice versa. We might make a mistake in the conversion of \[{m^2}\] to \[c{m^2}\]. We already know the conversion from m to cm.